APOLLONIUS OF PERGA CONICS PDF

Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry. His definitions of the terms ellipse , parabola , and hyperbola are the ones in use today. Apollonius worked on many other topics, including astronomy. Most of the work has not survived except in fragmentary references in other authors. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. For such an important contributor to the field of mathematics, scant biographical information remains.

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Apollonius of Perga , born c. Most of his other treatises are now lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria fl. As a youth, Apollonius studied in Alexandria under the pupils of Euclid, according to Pappus and subsequently taught at the university there.

He visited both Ephesus and Pergamum , the latter being the capital of a Hellenistic kingdom in western Anatolia , where a university and library similar to the Library of Alexandria had recently been built. In Alexandria he wrote the first edition of Conics , his classic treatise concerning the curves—circle, ellipse , parabola , and hyperbola—that can be generated by intersecting a plane with a cone; see figure.

Whereas his predecessors had used finite right circular cones, Apollonius considered arbitrary oblique double cones that extend indefinitely in both directions, as can be seen in the figure. The first four books of the Conics survive in the original Greek, the next three only from a 9th-century Arabic translation, and an eighth book is now lost.

Books I—IV contain a systematic account of the essential principles of conics and introduce the terms ellipse , parabola , and hyperbola , by which they became known. His genius is most evident in Book V, in which he considers the shortest and the longest straight lines that can be drawn from a given point to points on the curve. Such considerations, with the introduction of a coordinate system , lead immediately to a complete characterization of the curvature properties of the conics.

Many of the lost works were known to medieval Islamic mathematicians, however, and it is possible to obtain a further idea of their contents through citations found in the medieval Arabic mathematical literature. Sometimes known as the problem of Apollonius, the most difficult case arises when the three given things are circles. Apollonius demonstrated that parallel light rays striking the interior surface of a spherical mirror would not be reflected to the centre of sphericity, as was previously believed; he also discussed the focal properties of parabolic mirrors.

According to the mathematician Hypsicles of Alexandria c. According to the mathematician Eutocius of Ascalon c. Of particular interest was his determination of the points where, under general epicyclic motion, a planet appears stationary. See Ptolemaic system. Apollonius of Perga. Article Media. Info Print Cite. Submit Feedback.

Thank you for your feedback. Home Science Astronomy. See Article History. Read More on This Topic. The work of Apollonius of Perga extended the field of geometric constructions far beyond the range in the Elements Get exclusive access to content from our First Edition with your subscription.

Subscribe today. Learn More in these related Britannica articles:. The work of Apollonius of Perga extended the field of geometric constructions far beyond the range in the Elements. For example, Euclid in Book III shows how to draw a circle so as to pass through three given points or to be tangent to…. Apollonius reproduced known results much more generally and discovered many new properties of the figures.

He first proved that all conics are sections of any…. History at your fingertips. Sign up here to see what happened On This Day , every day in your inbox!

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Apollonius of Perga

We use cookies to give you a better experience. The ancient Greeks loved the simplicity and elegance of the line and the circle. In three-dimensional space, combining a circle with a fixed point not in the plane of the circle gives a cone, and it was by slicing this cone that Apollonius studied what were to become some of the most important curves in mathematics: the conic sections. He lived in Perga, which is in modern day Turkey, and wrote a series of books on conic sections, including the parabola, ellipse and hyperbola. Many of the facts discovered by him would surprise modern high school students for their elegance and richness.

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Apollonius and conic sections

His works had a very great influence on the development of mathematics and his famous book Conics introduced the terms parabola, ellipse and hyperbola. View one larger picture. Little is known of his life but his works have had a very great influence on the development of mathematics, in particular his famous book Conics introduced terms which are familiar to us today such as parabola , ellipse and hyperbola. Apollonius of Perga should not be confused with other Greek scholars called Apollonius, for it was a common name. In [ 1 ] details of others with the name of Apollonius are given: Apollonius of Rhodes, born about BC, a Greek poet and grammarian, a pupil of Callimachus who was a teacher of Eratosthenes ; Apollonius of Tralles, 2 nd century BC, a Greek sculptor; Apollonius the Athenian, 1 st century BC, a sculptor; Apollonius of Tyana, 1 st century AD, a member of the society founded by Pythagoras; Apollonius Dyscolus, 2 nd century AD, a Greek grammarian who was reputedly the founder of the systematic study of grammar; and Apollonius of Tyre who is a literary character.

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